Isomonodromic deformation of 𝑞-difference equations and confluence

Dreyfus, Thomas

doi:10.1090/proc/13173

Isomonodromic deformation of $q$-difference equations and confluence
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Proc. Amer. Math. Soc. 145 (2017), 1109-1120 Request permission

Abstract:

We study isomonodromic deformation of Fuchsian linear $q$- difference systems. Furthermore, we are looking at the behaviour of the Birkhoff connection matrix when $q$ goes to $1$. We use our results to study the convergence of the Birkhoff connection matrix that appears in the definition of the $q$-analogue of the sixth Painlevé equation.

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